Numerical study of steady and unsteady flow for power-law type generalized Newtonian fluids

This work deals with the numerical solution of laminar incompressible viscous flow for generalized Newtonian fluids in a branching channel. The governing system of equations is the system of generalized Navier–Stokes equations for incompressible viscous fluids flow. Generalized Newtonian fluids can be divided to two parts: shear thickening fluids and shear thinning fluids. Newtonian fluids are the special case with constant viscosity. For a viscosity function a power-law model is used. Numerical solution of the described model is based on cell-centered finite volume method using explicit Runge–Kutta time integration. The time-marching system of equations with steady boundary conditions is solved by finite volume method in conjunction with an artificial compressibility method. For the time integration an explicit multistage Runge–Kutta method of the second order of accuracy is used. In the case of unsteady computation two numerical methods are considered, artificial compressibility method and dual-time stepping method. Numerical results obtained by these methods are presented and compared.